You can copy your wallet over multiple machines, but you should generally not do that. Besides, your wallets would start drifting apart with each use - generally Bitcoin keeps a set of spare keys in case you need to use them in the future, and the set is refilled every now and then with random new keys.
The best practices for using Bitcoin is to have backups of wallets, but not use them on multiple machines at the same time. If you want to access your coins from anywhere, you can either look into running Bitcoin in a server mode (a bit tricky, not really for beginners), or using one of the many eWallets available around (you trust your coins to a third party, but this option is quite easy [just don't put too much money there;) ]).